#12046: Fix for numerator_ideal function
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Reporter: bleveque | Owner: davidloeffler
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-4.8
Component: number fields | Keywords: numerator, ideal, number field
Work_issues: | Upstream: N/A
Reviewer: | Author: Ben LeVeque
Merged: | Dependencies:
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Changes (by was):
* status: new => needs_review
Comment:
Replying to [comment:2 jdemeyer]:
> I still don't understand why you changed the documentation of the
`denominator_ideal()` method.
His modified version is much, much clearer as a definition. It's closer
to what you find if you look in more general commutative algebra books.
What was there before -- writing as N/D -- is more algorithmic, and
requires one to be in the special situation of Dedekind domain where
unique factorization of ideals holds. For example, if you define the
denominator ideal of x as the ideal of elements of Frac(R) that multiply x
into R, then this definition makes sense for any order R, even though we
do not have unique factorization of ideals in R. It is thus better as a
definition.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12046#comment:3>
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